An adaptive fuzzy semi-parametric regression model using TPB and ABC-BPNN

In this paper, a new hybrid method is developed that incorporates the rationale of truncated power basis (TPB) and artificial bee colony-back propagation neural networks (ABC-BPNN) into an adaptive fuzzy semi-parametric regression model yielding more accurate results and better generalization ability. The proposed adaptive fuzzy semi-parametric regression model comprises sub-model formulation and approximates the observed fuzzy outputs from the outside employing neural networks computation, such that the proposed adaptive fuzzy regression model better explains the inherent dependence and vagueness that exist in a given dataset. Using the cross-validation criterion and absolute deviation-based distance measures for LR-type fuzzy numbers, a target function optimization problem of constructing the adaptive fuzzy semi-parametric regression is performed by solving the smooth function, bandwidth of kernel function, and regression coefficients. This strategy significantly increases the goodness of fit for the proposed algorithm and offers a dependence framework among magnitude and uncertainty for the fuzzy regression model. We also use three formula measures to evaluate the fit quality of the regression results within each membership function as well as in the center or spread tendency property, respectively. The proposed algorithm is numerically evaluated on three experimental examples including a simulation study and two practical cases to prove its practicality and efficiency. Comparative analyses of our proposed method are provided to support its cogency, and the results show that our proposed model is more effective and stable than some other existing fuzzy regressions.